one trivial model to explain the zero probability of an | V V 〉 <math display="inline"><semantics> <mrow> <mo stretchy="false">|</mo> <mrow> <mi>V</mi> <mi>V</mi> </mrow> <mo stretchy="false">〉</mo> </mrow> </semantics></math> or | H H 〉 <math display="inline"><semantics> <mrow> <mo stretchy="false">|</mo> <mrow> <mi>H</mi> <mi>H</mi> </mrow> <mo stretchy="false">〉</mo> </mrow> </semantics></math> outcome would be to suppose that classical EM waves were always sent to the two detectors such that one wave was horizontally polarized and the other was vertically polarized. However, such an ad hoc model would not explain why such a preparation would correspond to this particular state, and it would not be generalizable to other evident anti-correlations from the very same state. The above quantum example also would exhibit anti-correlations if each photon were measured in the same diagonally polarized basis, while the ad hoc classical model would not.

We believe that this step has already beentaken, but not fully acknowledged, by a substantial part of the quantum-opticscommunity. For example, three review articles (2−4) on light squeezing makeextensive use of phase-space diagrams, and one of them(3) states explicitly thatthe photon description of the light field is not helpful in the understanding ofthe phenomenon

The quantum harmonic oscillator is the quantum analog of the classical harmonic oscillator and is one of the most important model systems in quantum mechanics. This is due in partially to the fact that an arbitrary potential curve V(x)V(x)V(x) can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point. Furthermore, it is one of the few quantum-mechanical systems for which an exact, analytical solution exists. Solving other potentials typically require either approximations or numerical approaches to identify the corresponding eigenstates and eigenvalues (i.e., wavefunctions and energies).

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